The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is _ _ _ _ cm.

Step-by-step solution

The magnification of a thin lens is given by m = f f + u . Given that the size of the images is equal for two different object positions, the magnitudes of the magnifications must be equal: |m₁| = |m₂| . For a single lens to produce images of the same size at two different object distances, one image must be real and the other must be virtual. Let u₁ = -8 cm and u₂ = -24 cm. Then, m₁ = -m₂ (since one is real and one is virtual). f f + u₁ = - f f + u₂ 1 f - 8 = - 1 f - 24 f - 24 = -(f - 8) f - 24 = -f + 8 2f = 32 f